Reported controlled double-slit electron diffraction with single-electron detection (Bach, Pope, Liou and Batelaan)

The source is the primary preprint of Bach, Pope, Liou and Batelaan (arXiv:1210.6243v1, 22 October 2012), reporting a controlled double-slit electron diffraction experiment. The reported apparatus consists of a thermionic tungsten filament with electrostatic lenses producing an electron beam of energy 600 eV; a collimation aperture of 2 micrometre width and 10 micrometre height placed 16.5 cm from the source; a double-slit 30.5 cm beyond the collimation aperture, milled with a 30 keV Ga+ focused-ion-beam system into a 100 nm silicon-nitride membrane coated with about 2 nm of gold, with two slits of 50 nm width, 280 nm centre-to-centre separation and 4 micrometre height, each with a 150 nm support midway; a movable mask 5 micrometre wide, driven by a piezoelectric actuator and placed 230 micrometre downstream of the double-slit; an electrostatic quadrupole lens magnifying the pattern; and a two-dimensional microchannel plate and phosphor screen imaged by a CCD camera. The body of the paper gives the mask height as 10 micrometre while the caption of figure 1 gives 20 micrometre; the inconsistency is recorded and not resolved here. The comparison is a reported experiment of the framework in the sense of the preparation and apparatus postulate Preparation and apparatus postulate P7: declared preparations, isolation and sampling assumptions; the identification of the reported device with the quantities of any model's preparation or detection is an apparatus identification carrying the source's limitations.

Two procedures are reported. First, for the slit-control measurements the mask is moved across the double-slit so that predominantly one slit, then both slits, then the other slit transmit; the recorded image frames for each mask position are summed and the accumulated image normalized, producing the distributions labelled P1 (slit 1), P12 (both slits) and P2 (slit 2). Second, for the build-up measurement the mask is centred, the source intensity is reduced until the detection rate in the pattern is about 1 Hz, the quadrupole lens is set to magnify the central five diffraction orders, and localized detections are recorded with a blob-localization scheme; the reported final accumulation took about 2 hours. The paper reports an average distance between consecutive electrons of 2.3e6 m at this rate and energy, and states that this ensures at most one electron is present in the 1 m apparatus at any time. No arrival-process law, occupancy bound, event-selection rule, dead-time model or independence test is reported, so that statement remains a reported apparatus-behaviour inference; no finite-sampling analysis under a declared independent-trials model is performed here or in the source.

The paper reports, and the retained figures show, slit-selective probability distributions: a single-slit central diffraction order in the P1 and P2 configurations and a double-slit distribution in the P12 configuration, with weak double-slit contributions visible in the first diffraction order of the nominal single-slit configurations, which the paper attributes to the finite separation between the mask and the double-slit. For the mask-centred build-up the figure captions report accumulated localized-event counts of 2, 7, 209, 1004 and 6235 in five successive images of the central five orders, the paper describing the earliest images as appearing random and a pattern becoming discernible at the largest counts, with a clearly visible pattern in the final image. Each reported detection is a localized blob whose size represents the localization error of the detection scheme; the accumulated distribution, not any single event, carries the reported pattern.

The report supplies no numerical uncertainty budget for its observations. In detail: no calibrated detector efficiency or background map is given; no numerical value of the localization error is given although the blob size is said to represent it; no uncertainty is given for the beam energy, the slit dimensions or the mask position; no statistical independence of the recorded events is tested; no event-selection or image-processing error rate is quantified; and no significance level, confidence interval or fitted comparison with a competing distribution is reported. The mask-height inconsistency between the body text and the figure caption is unresolved. The reported claim that at most one electron is present at a time rests on the average-separation estimate and not on a bound on the probability of two electrons in the apparatus. The approximate rate of about 1 Hz and duration of about 2 hours are not converted here into a trial count, efficiency or calibrated rate, and no uncertainty is manufactured for them.

The source interprets the slit-selective patterns and the build-up of a diffraction pattern from localized detections as a realization of Feynman's two-slit thought experiment, illustrating interference and wave-particle duality for electrons. Read as a report, the accumulated distributions and their dependence on which slits transmit are consistent with a coherent electron-amplitude model under the reported preparation and apparatus conditions; the report's own comparison is qualitative and no competing incoherent or classical model is specified, fitted or tested, so the report does not by itself discriminate between such models. Classical wave models also exhibit interference, so a reported pattern does not establish the quantum framework or exclude every alternative; conversely, nothing here falsifies a model, and each recorded event remains a localized detection whose relation to any theoretical amplitude is a model identification. A controlled test of the declared two-path law Coherent and which-path detection laws of the declared two-path model would require a declared preparation model, a declared detector response including efficiency, resolution and background, a declared competing law, and a declared sampling model with its statistical method; none of these is supplied by this report, and no such analysis is performed here. Agreement of the reported distributions with a model would be evidence about the combined model, apparatus and analysis assumptions, not a proof of the model.